{
  "cells": [
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "13vIU-X_e-KH",
        "outputId": "93ef0131-7514-48d3-ce0e-3e67e1eb840c"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x10b79748>]"
            ]
          },
          "execution_count": 1,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "iVBORw0KGgoAAAANSUhEUgAAAiMAAAGdCAYAAADAAnMpAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjMuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8vihELAAAACXBIWXMAAA9hAAAPYQGoP6dpAABF7klEQVR4nO3de1xUdf4/8NeZYS4gMIDIVRTUvCAK3iAyu+yXVr8W1m+/+82tTfv6Lds13Ucrv93KysjaTWurb7tm+lvLtd+vWt3askyXLpjbVhQqYJKoKSAoDKDAcGdg5vz+GM4oAsIMzJw5M6/n48GjOpwZ3pyGOa/5XAVRFEUQERERyUQldwFERETk2xhGiIiISFYMI0RERCQrhhEiIiKSFcMIERERyYphhIiIiGTFMEJERESyYhghIiIiWfnJXcBQWK1WVFVVISgoCIIgyF0OERERDYEoimhubkZMTAxUqoHbPxQRRqqqqhAXFyd3GUREROSEyspKjB07dsDvKyKMBAUFAbD9MsHBwTJXQ0REREPR1NSEuLg4+318IIoII1LXTHBwMMMIERGRwgw2xIIDWImIiEhWDCNEREQkK4YRIiIikhXDCBEREcmKYYSIiIhkxTBCREREsmIYISIiIlkxjBAREZGsFLHoGRF5J4tVRH5ZPWqbOxARpEdqQhjUKu4/ReRrHG4Z+eKLL5CZmYmYmBgIgoA9e/YM+piDBw9i9uzZ0Ol0mDRpEnbu3OlEqUTkTXKKq3H9cwdw1/Zv8NCuIty1/Rtc/9wB5BRXy10aEbmZw2GktbUVycnJ2LJly5DOLysrw6233oqbb74ZRUVF+PWvf437778fH3/8scPFEpF3yCmuxqo3C1Bt6uh13GjqwKo3CxhIiHyMIIqi6PSDBQHvv/8+7rjjjgHPeeSRR7Bv3z4UFxfbj/3sZz9DY2MjcnJyhvRzmpqaYDAYYDKZuDcNkcJZrCKuf+5AnyAiEQBEGfT48pEfscuGSOGGev92+QDWvLw8ZGRk9Dq2cOFC5OXlDfiYzs5ONDU19foiIu+QX1Y/YBABABFAtakD+WX17iuKiGTl8jBiNBoRGRnZ61hkZCSamprQ3t7e72M2btwIg8Fg/4qLi3N1mUTkJrXNAwcRZ84jIuXzyKm969atg8lksn9VVlbKXRIRjZCIIP2InkdEyufyqb1RUVGoqanpdaympgbBwcHw9/fv9zE6nQ46nc7VpRGRDFITwhBt0A86ZiQ1Icy9hRGRbFzeMpKeno7c3Nxexz799FOkp6e7+kcTkQdSqwQsTx9/1XOyMxM5eJXIhzgcRlpaWlBUVISioiIAtqm7RUVFqKioAGDrYlm+fLn9/F/+8pcoLS3Fww8/jBMnTuDVV1/F3/72N6xdu3ZkfgMiUhRRFPHJcVtrqb+m71vQbxdOxqKkaHeXRUQycrib5vDhw7j55pvt/52VlQUAuPfee7Fz505UV1fbgwkAJCQkYN++fVi7di3++Mc/YuzYsXjttdewcOHCESifiJTmw6NVKKxoRIBWjc+ybsTZi22obe7AnsLz+PxkHT45Xotf3jgJKraMEPmMYa0z4i5cZ4TIO7SbLfi3Fw+iytSB3/x4Mtb86Br792qbO3DzHw6i1WzB/yxNxv+aNVbGSoloJHjMOiNERJI/f1GKKlMHYkP8cf+CCb2+FxGkx+ofTQIAPPePk2gzd8tRIhHJgGGEiNyi2tSObf88AwB49N+nQq9R9znnv+cnYGyoP4xNHfg//yx1d4lEJBOGESJyiz/knER7lwVzx4fitpn9D1DVa9R4bPE0AMD/+eIMqhr7XxiRiLwLwwgRuVxRZSPeKzwPAHgyMxGCMPDg1H9PikJqfBg6uqx4PueEu0okIhkxjBCRS4miiKf3fg8A+I/ZYzFzbMhVzxcEoSewAHuKqlBQ0eCGKolITgwjRORSe7+rRkFFI/w1ajy8aMqQHpMUa8B/zrHNpnl673FYrR4/6Y+IhoFhhIhcpt1swab9JQCAB2+aiMjgoe8385sfT8EorRpFlY348GiVq0okIg/AMEJELrP9X5em8q68YcLgD7hMRLAeD95sm+q76R8nONWXyIsxjBCRSxhNHdh68OpTeQdz3/UJiA2xTfX98xec6kvkrRhGiMglnv/4BNq7LJhzlam8g7l8qu+2f3KqL5G3YhghohF3tLIR7xX0TOW97epTeQezeAan+hJ5O4YRIhpRoiji6Y+OAwB+MjsWyXEhw3o+QRCw/jZO9SXyZgwjRDSi9n5XjSNnG2xTeRdOHZHnnDHWgJ/OvjTVVwH7exKRAxhGiGjEdHT1nsobZRj6VN7B/HbhFARwqi+RV2IYIaIRs71nV94Yg97hqbyDiQjWYzWn+hJ5JYYRIhoRNU0deFWayrt4mlNTeQcjTfWtNnGqL5E3YRghohHxfM+uvLPHhSDTyam8g7lyqm+1iVN9ibwBwwgRDdvRykb8veAcACA7c/qwpvIOZvGMKMyLD+2Z6nvSZT+HiNyHYYSIhmWkp/IORhAEPHnbdAgC8H7heRRyqi+R4jGMENGwfOSCqbyDmTHWgP+Qpvp+xKm+RErHMEJETuvosmDTP2yroq4a4am8g5Gm+hZWcKovkdIxjBCR0177VynON7bbpvIuGNmpvIOJvGKqb7vZ4tafT0Qjh2GEiJxy+VTeR/59Kvy1Iz+VdzCc6kvkHRhGiMgpz+ecRJvZNpV3SXKMLDXoNWqsW2wbp8KpvkTKxTBCRA777tylqbxPungq72BunRGNueND0d5l4VRfIoViGCEih4iiiKf39kzlnRWLFBdP5R2MIAh4MjMRAKf6EikVwwgROWTfsWoc7pnK+9tFU+QuBwAwc2wIp/oSKRjDCBENWUeXBRv326by/vLGiYg2+Mtc0SUPL+JUXyKl8pO7ACLybBariPyyetQ2d+Dr0xftU3kfGOFdeYcrMliPB2+aiBc+OYVN/zgBg78GpvYuRATpkZoQBrVKvnEtRHR1DCNENKCc4mps2Hsc1aaOXsf/PSlKlqm8g7l/wQTs+Koc1aYO/NdfDtmPRxv0yM5MxKIk12zgR0TDw24aIupXTnE1Vr1Z0CeIAMDrX5Ujp7hahqqu7uDJWtS3mvscN5o6sOrNAo+smYgYRoioHxariA17j2OgYaACgA17j8Ni9ZyBolLN/ZGq9LSaiciGYYSI+sgvq++3RUQiAqg2dSC/rN59RQ1CiTUTkQ3DCBH1Uds88E3dmfPcQYk1E5ENwwgR9RERNLTdd4d6njsosWYismEYIaI+UhPCEG3QY6DJsAJsM1RSE8LcWdZVKbFmIrJhGCGiPtQqAdk9S6xfSbrZZ2cmetTaHZfXPFBVnlYzEdkwjBBRvxYlReOPP0vpczzKoMfWe2Z75Jodi5KisfWe2Ygy9O6KCdL7eWzNRMRFz4joKiKCbTf1kAANnspMRGSwv8evZrooKRq3JEYhv6wef80/iw+PViMtYTSDCJEHYxghogFJ02CvnxSOO2aNlbmaoVOrBKRPHA2dRoUPj1bj8Nl6WK0iVB4cooh8GbtpiGhAUhhJmzBa5kqcMyPWAH+NGo1tXfihtkXucohoAAwjRNSvLosVR842AADSFDoDRaNWYc74UADAt2UXZa6GiAbCMEJE/Tp23oT2LgtCAzSYNCZQ7nKcJk3l/ZYrrxJ5LIYRIuqX1EUzLz5M0WMtpDCSX1YPUeS+NESeiGGEiPolhRGlLxKWEhcCrVqFuuZOlF9sk7scIuoHwwgR9WGxijjUE0auVejgVYleo0ZKXAgA4NtSjhsh8kQMI0TUR0l1E5o7uxGo88O06GC5yxm2y7tqiMjzMIwQUR/STXtufKhHL3A2VBzESuTZGEaIqA9vGS8imTPeFqrON7bjXAPHjRB5GoYRIupFFEXkl/csdpag7PEiklE6PyTFGgAAh8rZOkLkaRhGiKiX07UtqG81Q69RYUbPDdwbSAu3fVvKMELkaRhGiKgXaVzF7HGh0Pp5z1tEajwHsRJ5Ku95pyGiEeFt40Uk8+LDIAhA6YVW1DZ3yF0OEV2GYYSI7ERRtO/h4i3jRSSGAA2mRtmmKR8qa5C5GiK6HMMIEdlV1LehpqkTGrWAWeNC5C5nxNnHjXDTPCKPwjBCRHbSeJHksSHQa9QyVzPyuPgZkWdiGCEiO28dLyKRfq8TxmY0tpllroaIJE6FkS1btiA+Ph56vR5paWnIz8+/6vkvv/wypkyZAn9/f8TFxWHt2rXo6OAAMiJPYx8vovD9aAYSHqjDxDGjAACHyjluhMhTOBxGdu/ejaysLGRnZ6OgoADJyclYuHAhamtr+z3/7bffxqOPPors7GyUlJTg9ddfx+7du/HYY48Nu3giGjlVje2orG+HSrCtWOqtUnsG5nLTPCLP4XAYeemll7By5UqsWLECiYmJ2LZtGwICArBjx45+z//6668xf/583H333YiPj8ePf/xj3HXXXYO2phCRe0krkybFGhCo85O5GteRBrHmcyVWIo/hUBgxm804cuQIMjIyLj2BSoWMjAzk5eX1+5jrrrsOR44csYeP0tJS7N+/H4sXLx7w53R2dqKpqanXFxG5ljR4VVoczFtJ40aKz5vQ0tktczVEBDgYRi5cuACLxYLIyMhexyMjI2E0Gvt9zN13342nn34a119/PTQaDSZOnIibbrrpqt00GzduhMFgsH/FxcU5UiYROUHqtvDW8SKSmBB/xIX5wyoCR85y3AiRJ3D5bJqDBw/i2WefxauvvoqCggK899572LdvH5555pkBH7Nu3TqYTCb7V2VlpavLJPJpF1o6caauFQAwL957x4tIUuM5boTIkzjUMRweHg61Wo2amppex2tqahAVFdXvY9avX49ly5bh/vvvBwDMmDEDra2teOCBB/D4449Dpeqbh3Q6HXQ6nSOlEdEwHOrpopkaFYSQAK3M1bheWkIY/l5wjuuNEHkIh1pGtFot5syZg9zcXPsxq9WK3NxcpKen9/uYtra2PoFDrbYtpiSKoqP1EpELfOvl64tcKW2C7fc8eq4RHV0WmashIoe7abKysrB9+3a88cYbKCkpwapVq9Da2ooVK1YAAJYvX45169bZz8/MzMTWrVuxa9culJWV4dNPP8X69euRmZlpDyVEJC8pjHjbfjQDGRcWgMhgHbosIgorGuUuh8jnOTx/b+nSpairq8OTTz4Jo9GIlJQU5OTk2Ae1VlRU9GoJeeKJJyAIAp544gmcP38eY8aMQWZmJn7/+9+P3G9BRE4ztXXhhNE2Y21egvePFwEAQRCQmjAae49WIb+sHukTfSOEEXkqQVRAX0lTUxMMBgNMJhOCg4PlLofIq+SW1OC+Nw5jQvgoHPjNTXKX4zb/75uzWL+nGNdNHI23V14rdzlEXmmo92/uTUPk47x9P5qBXNvz+xZUNMDcbZW5GiLfxjBC5OO+8dEwMikiEGGjtOjosuLYeZPc5RD5NIYRIh/W2tmN4p4bsbcvdnYlQRDsa6pwii+RvBhGiHxYQUUDLFYRsSH+iA3xl7sct7NvmlfGxc+I5MQwQuTD8u1Ten2ri0Yi/d6Hy22hjIjkwTBC5MO+LfXN8SKSadHBCNL5oaWzGyXV3JCTSC4MI0Q+qqPLgqLKRgC+N15EolYJmNszbuRbjhshkg3DCJGPOlrZCLPFijFBOsSPDpC7HNnYx41w0zwi2TCMEPmoy9cXEQRB5mrkI+1Tc6i8HlaOGyGSBcMIkY/61scHr0qSYgzw16jR0NaF03UtcpdD5JMYRoh8UJfFiiNnGwD4zuZ4A9H6qTB7fAgAjhshkgvDCJEPKj5vQnuXBSEBGlwTESh3ObJLjbcFMi5+RiQPhhEiHyTddOfFh0Gl8t3xIhJp3Mi3pRehgL1DibwOwwiRD/L1xc6ulBIXAq1ahdrmTpy92CZ3OUQ+h2GEyMdYrCLyy6Uw4tvjRSR6jRrJcQYA7KohkgPDCJGPOWFsQnNHNwJ1fpgWHSR3OR5DWoWWg1iJ3I9hhMjHSJ/854wPhZ+abwGSNG6aRyQbvhMR+ZjLFzujS2aPD4VaJeBcQzvON7bLXQ6RT2EYIfIhoijaw8i1ExhGLheo80NSTDAA4BC7aojcimGEyIecqWvBxVYzdH4qzIgNkbscj8NxI0TyYBgh8iHSTXb2uFBo/fjnfyWOGyGSB9+NiHwIx4tc3bz4MAgCUFrXirrmTrnLIfIZDCNEPkIURXxb2rO+CMeL9MsQoMGUSNt050Pl7KohcheGESIfUVnfDmNTBzRqAbPiQuUux2NJq9Jy8TMi92EYIfIR0jiImWND4K9Vy1yN50qbYBs38k0px40QuQvDCJGP4HiRoZkXb7s+J2ua0dhmlrkaIt/AMELkI75lGBmSMUE6TBgzCqIIHC5vkLscIp/AMELkA6pN7aiob4NKAOaO53iRwdjHjXAQK5FbMIwQ+QCpi2Z6jAFBeo3M1Xi+S+uNMIwQuQPDCJEP4HgRx0jXqfi8CS2d3TJXQ+T9GEaIfADHizgmJsQfY0P9YbGKKDjLcSNErsYwQuTlLrR04nRtCwAgNZ5hZKhSud4IkdswjBB5ucM9gzCnRAYhdJRW5mqU49qecSMMI0SuxzBC5OXYReMc6XoVVTaio8siczVE3o1hhMjLSfvRMIw4ZvzoAEQE6WC2WFFU2Sh3OURejWGEyIuZ2rtQYmwCcGntDBoaQRA4boTITRhGiLzYkbP1EEUgIXwUIoL1cpejONI+NQwjRK7FMELkxezjRTiLxilSa9KRsw3oslhlrobIezGMEHkxjhcZnkljAhEaoEF7lwXHzpvkLofIazGMEHmp1s5uFPfcQNMmMIw4Q6US7Lv4squGyHUYRoi8VGFFI7qtImJD/DE2NEDuchSL40aIXI9hhMhL5ZddBMAumuGSxo0cKquHxSrKXA2Rd2IYIfJS33CxsxExLToYgTo/NHd2o6S6Se5yiLwSwwiRF+rostgX6uL6IsOjVgmYGx8KgF01RK7CMELkhb47Z4K524rwQB0SwkfJXY7ipXGfGiKXYhgh8kLSeJG0hDAIgiBzNcpnX4m1vB6iyHEjRCONYYTIC3FzvJE1I9YAvUaF+lYzTte2yF0OkddhGCHyMl0WK46cbQDAMDJStH4qzB5nGzfyLbtqiEYcwwiRl/m+qgltZgsM/hpMiQySuxyvwXEjRK7DMELkZaTxIvPiw6BScbzISLl8B1+OGyEaWQwjRF5G2o+GU3pH1qxxIdCoBRibOlBR3yZ3OURehWGEyItYrCLyyzl41RX0GjWSx4YA4LgRopHGMELkRU4am9Hc0Y1RWjWmxwTLXY7XkTYc5LgRopHFMELkJSxWEbsPVQIAJkYEcn0RF0jtGcT6xak6fFB0HnlnLnK/GqIR4Cd3AUQ0fDnF1diw9ziqTR0AbCuwXv/cAWRnJmJRUrTM1XmPhtZOAEBtcyce2lUEAIg26HmdiYaJLSNECpdTXI1VbxbYg4jEaOrAqjcLkFNcLVNl3iWnuBprdx/tc5zXmWj4nAojW7ZsQXx8PPR6PdLS0pCfn3/V8xsbG7F69WpER0dDp9Nh8uTJ2L9/v1MFE9ElFquIDXuPo7+OAunYhr3H2ZUwTLzORK7lcBjZvXs3srKykJ2djYKCAiQnJ2PhwoWora3t93yz2YxbbrkF5eXlePfdd3Hy5Els374dsbGxwy6eyNfll9X3aRG5nAig2tTBAZfDxOtM5FoOjxl56aWXsHLlSqxYsQIAsG3bNuzbtw87duzAo48+2uf8HTt2oL6+Hl9//TU0Gg0AID4+fnhVExEAoLZ54BukM+dR/3idiVzLoZYRs9mMI0eOICMj49ITqFTIyMhAXl5ev4/58MMPkZ6ejtWrVyMyMhJJSUl49tlnYbFYBvw5nZ2daGpq6vVFRH1FBOlH9DzqH68zkWs5FEYuXLgAi8WCyMjIXscjIyNhNBr7fUxpaSneffddWCwW7N+/H+vXr8eLL76I3/3udwP+nI0bN8JgMNi/4uLiHCmTyGekJoQh2jDwDVCAbbYHF0AbHuk6DzRZmteZaHhcPpvGarUiIiICf/7znzFnzhwsXboUjz/+OLZt2zbgY9atWweTyWT/qqysdHWZRIqkVgnIzkzs93vSjTM7MxFq7lEzLJdf5yuvJK8z0fA5FEbCw8OhVqtRU1PT63hNTQ2ioqL6fUx0dDQmT54MtVptPzZt2jQYjUaYzeZ+H6PT6RAcHNzri4j6tygpGjdcE97neJRBj633zOb6FyNkUVI0tt4zG1FXtERFBOt4nYmGyaEBrFqtFnPmzEFubi7uuOMOALaWj9zcXKxZs6bfx8yfPx9vv/02rFYrVCpb9jl16hSio6Oh1WqHVz0RAQCMTbaBk1kZkzE+PAARQbYuA35SH1mLkqJxS2IU8svqsfqtI6hv68IffpqMGyaPkbs0IkVzuJsmKysL27dvxxtvvIGSkhKsWrUKra2t9tk1y5cvx7p16+znr1q1CvX19XjooYdw6tQp7Nu3D88++yxWr149cr8FkQ9raDXjVE0LAODn147D7SmxSJ84mkHERdQqAekTR+PGKREAgMNnG2SuiEj5HJ7au3TpUtTV1eHJJ5+E0WhESkoKcnJy7INaKyoq7C0gABAXF4ePP/4Ya9euxcyZMxEbG4uHHnoIjzzyyMj9FkQ+TLoZThwzCqMDdTJX4zvmxYfh/cLzOMS1RYiGzam9adasWTNgt8zBgwf7HEtPT8c333zjzI8iokEcKrfdDDmTw73mxYcCAAorG2DutkLrx901iJzFvx4ihZNW/ZwXzzDiTpMiAhEaoEFHlxXFVSa5yyFSNIYRIgVrM3ej+LztRsgw4l6CIGBuzzVnVw3R8DCMEClYUUUjuq0iooL1GBvqL3c5PidVCiPlDCNEw8EwQqRg+T03wXkJYRAEzp5xt3kJUhhpgJU79hI5jWGESMHsg1d7BlOSe02PCYa/Rg1Texd+qG2RuxwixWIYIVKoLosVBWcbAVz6hE7upVGrMHt8CIBLrVRE5DiGESKFOl7VhPYuCwz+GkyOCJK7HJ81j4NYiYaNYYRIoaQumrnjQ6HiaquyuXwQqyhy3AiRMxhGiBTKvr4Iu2hkNWtcKPxUAqpNHTjX0C53OUSKxDBCpECiKNqXgef6IvLy16qRFGsAABw+y64aImcwjBAp0Jm6FtS3mqHXqDCj50ZI8pGW4s8v46Z5RM5gGCFSIOmmlxIXwj1RPMA8Ln5GNCx8FyNSoEvri7CLxhPMHW9b5+V0ra3FiogcwzBCpEAcvOpZQkdpMTkyEABbR4icwTBCpDBVje0439gOtUrA7HFcedVTcNM8IucxjBApjPTJe3pMMEbp/GSuhiTcNI/IeQwjRApj76LheBGPInWZFVc1obWzW+ZqiJSFYYRIYaRP3gwjniU2xB+xIf6wWEUUVjTKXQ6RojCMEClIQ6sZp2psu8PO5U69Hmdez/8TbppH5BiGESIFkVZdnTBmFMIDdTJXQ1eSumo4iJXIMQwjRArC9UU8m/T/pbCyAeZuq8zVECkHwwiRgnC8iGebFBGI0AANOrqsKK4yyV0OkWIwjBApRLvZgmPnbDe4VC525pEEQeB6I0ROYBghUojCygZ0W0VEBesxNtRf7nJoAFxvhMhxDCNECnGoZ3O8eQlhEARB5mpoIPZBrOUNsFpFmashUgaGESKFuDR4lVN6Pdn0mGD4a9QwtXfhh9oWucshUgSGESIF6LZYUVBxqWWEPJdGrcLs8SEAuN4I0VAxjBApwPdVTWgzW2Dw12ByRJDc5dAgpNlOhxlGiIaEYYRIAaQumrnjQ6FScbyIp0vljBoihzCMECmAfXM8dtEoQsq4EPipBFSZOnCuoU3ucog8HsMIkYcTRdG+DDwXO1OGAK0fpscaAHCKL9FQMIwQebgzdS2obzVDr1FhRs8NjjyfNOspv2dKNhENjGGEyMNJN7OUuBBo/fgnqxTzuPgZ0ZDxnY3Iw3FzPGWSwsjpWlvLFhENjGGEyMNx8KoyhY7S4pqIQABsHSEaDMMIkQeramzH+cZ2qFUCZo3jyqtKY18anlN8ia6KYYTIg0mfqBOjgxGo85O5GnIUN80jGhqGESIPJt3EOKVXmaSWkeKqJrR2dstcDZHnYhgh8mDSTr2pCeyiUaLYEH/EhvjDYhVRWNEodzlEHothhMhDNbaZcbKmGQAwly0jijVPWm+EXTVEA2IYIfJQh8ttrSITxoxCeKBO5mrIWRzESjQ4hhEiD8X1RbyD9P+vsLIB5m6rzNUQeSaGESIPlc/Bq15hUkQgQgM06OiyorjKJHc5RB6JYYTIA7WbLTh2znbjSuViZ4omCIJ9zA+7aoj6xzBC5IEKKxvQbRURFazH2FB/ucuhYZIGsXK9EaL+MYwQeSBpSu+8hDAIgiBzNTRcUlfb4bMNsFpFmash8jwMI0Qe6NLgVa4v4g2SYg3w16jR2NaF03UtcpdD5HEYRog8TLfFioKKSy0jpHwatQqzxoUAuLTxIRFdwjBC5GG+r2pCm9kCg78GkyOC5C6HRsg87lNDNCCGESIPI92s5o4PhUrF8SLeIpWLnxENiGGEyMNIzfjsovEus8aFwE8loMrUgXMNbXKXQ+RRGEaIPIgoijh8tme8CBc78yoBWj9MjzUAYFcN0ZUYRog8yJm6VtS3mqHXqDCj58ZF3kOaHZXfM3WbiGwYRog8iPSJOSUuBFo//nl6Gw5iJeof3+2IPIg0uJFdNN5J+v96urYF9a1mmash8hwMI0QehJvjebfQUVpcExEIgK0jRJdzKoxs2bIF8fHx0Ov1SEtLQ35+/pAet2vXLgiCgDvuuMOZH0vk1apN7TjX0A6VAMwez5VXvdU8TvEl6sPhMLJ7925kZWUhOzsbBQUFSE5OxsKFC1FbW3vVx5WXl+M3v/kNFixY4HSxRN5MmtI7PcaAQJ2fzNWQq6Ry3AhRHw6HkZdeegkrV67EihUrkJiYiG3btiEgIAA7duwY8DEWiwU///nPsWHDBkyYMGFYBRN5q0PsovEJUstIcVUTWju7Za6GyDM4FEbMZjOOHDmCjIyMS0+gUiEjIwN5eXkDPu7pp59GREQE7rvvviH9nM7OTjQ1NfX6IvJ20k69qQnsovFmsSH+iDHoYbGKKKxolLscIo/gUBi5cOECLBYLIiMjex2PjIyE0Wjs9zFffvklXn/9dWzfvn3IP2fjxo0wGAz2r7i4OEfKJFKcxjYzTtY0AwDmsmXE60mtI/nsqiEC4OLZNM3NzVi2bBm2b9+O8PDwIT9u3bp1MJlM9q/KykoXVkkkv8PltlaRCWNGITxQJ3M15Gr29UY4iJUIAODQKLnw8HCo1WrU1NT0Ol5TU4OoqKg+5585cwbl5eXIzMy0H7NarbYf7OeHkydPYuLEiX0ep9PpoNPxDZl8hzReJJWtIj5B2jSvsLIB5m4rF7gjn+fQX4BWq8WcOXOQm5trP2a1WpGbm4v09PQ+50+dOhXHjh1DUVGR/WvJkiW4+eabUVRUxO4Xoh5cX8S3TBoTiJAADTq6rPi+yiR3OUSyc3j+YFZWFu69917MnTsXqampePnll9Ha2ooVK1YAAJYvX47Y2Fhs3LgRer0eSUlJvR4fEhICAH2OE/mqdrMFx87Zbkip3KnXJ6hUAuaOD8NnJTU4VF6PWeM4aJl8m8NhZOnSpairq8OTTz4Jo9GIlJQU5OTk2Ae1VlRUQKVikyPRUBVWNqDbKiIqWI+xof5yl0NukpoQis9KapBf1oAHbpC7GiJ5ObWy0po1a7BmzZp+v3fw4MGrPnbnzp3O/EgiryVN6Z2XEAZBEGSuhtxF6pI7fLYeVqsIlYr/78l3sQmDSGaHz0qDV9lU70uSYg3w16jR2NaF03UtcpdDJCuGESIZdVusKDh7qWWEfIdGrcKscSEALm0FQOSrGEaIZHS8ugmtZgsM/hpMjgiSuxxys3ncp4YIAMMIkaykT8Rzx4dyzIAPSuUOvkQAGEaIZCV9IuYS8L5p1rgQ+KkEVJk6cK6hTe5yiGTDMEIkE1EU7cvAc3M83xSg9cP0WAMAdtWQb2MYIZLJmbpWXGw1Q+enwozYELnLIZlIs6jye6Z4E/kihhEimUifhFPiQrg3iQ+by0GsRAwjRHKRBi1yCXjfJs2oOV3bgvpWs8zVEMmDYYRIJtwcjwAgbJQWkyICAbB1hHwXwwiRDKpN7TjX0A6VAMwez8Grvs6+3gin+JKPYhghkoG0vsj0GAMCdU5tEUVeRJpNxZYR8lUMI0QyOMQuGrqM9DoormpCa2e3zNUQuR/DCJEbWawi8s5cRG5JLQDbyqtEY0MDEG3Qw2IVseXz08g7cxEWqyh3WURuw/ZhIjfJKa7Ghr3HUW3qsB97au/3UKmARUnRMlZGcssprkZDm20mzasHz+DVg2cQbdAjOzORrw3yCWwZIXKDnOJqrHqzoFcQAYC65k6serMAOcXVMlVGcpNeGx1d1l7HjaYOvjbIZzCMELmYxSpiw97j6K/RXTq2Ye9xNsv7IL42iGwYRohcLL+svk+LyOVEANWmDvsMG/IdfG0Q2TCMELlYbfPANxtnziPvwdcGkQ3DCJGLRQTpR/Q88h58bRDZMIwQuVhqQhiiDXoIA3xfABBt0HOPGh/E1waRDcMIkYupVQKyMxP7HaQo3YSyMxOhVg10SyJvJb02AAwYSPjaIF/AMELkBouSonF7Skyf41EGPbbeM5trSfiwRUnR2HrPbEQZenfFqATglbtn8bVBPoGLnhG5gSiKOF7VBAD4xQ0TkBgTjIggW/M7P/XSoqRo3JIY1TO7ph1PfvA9Wjq7EaTXyF0akVswjBC5QUl1M36obYHWT4XVP5qEYN5k6ApqlYD0iaMBAAUVDXjzmwp8UFSFGyaPkbkyItdjNw2RG3xQdB4A8G9TIxhEaFC3p8QCAD7+3oiOLovM1RC5HsMIkYtZrSI+PFoF4NJNhuhq5owLRWyIP1o6u/FZSY3c5RC5HMMIkYt927PKZpDeDzdPZZM7DU6lEuwDnvcUVslcDZHrMYwQudiHR21dNIuToqHzU8tcDSnFHbNsrWj/PFWLxp4dfYm8FcMIkQt1dluw7zvbrqu3z+o7tZdoIJMjgzA1KghdFhH7jxnlLofIpRhGiFzo4Mk6NHV0IypYj2sTRstdDimM1Dqyp2cANJG3YhghciFpFs2SlBiouJ4IOWhJsq01Lb+sHucb22Wuhsh1GEaIXKS5owufldQCuHRTIXJETIi/fV+avUc5kJW8F8MIkYvkFBth7rZiUkQgpscEy10OKdQdPdPB9xSyq4a8F8MIkYt8UGT7JHtHSgwEgV005JzFM6KgUQs4YWzGSWOz3OUQuQTDCJEL1DZ14OszFwAAS5K50Bk5LyRAi5umRADgQFbyXgwjRC6w97tqWEVg9rgQjBsdIHc5pHDSAmgfFlXBahVlroZo5DGMELmANItGmppJNBwZ0yIRqPPD+cZ2HKlokLscohHHMEI0wkrrWvDdORPUKgG3zoiWuxzyAnqNGgunRwHgQFbyTgwjRCNsT8/A1QXXhGN0oE7mashb3NGzgu++Y9Uwd1tlroZoZDGMEI0gURTxodRFwx16aQSlTxiN8EAdGtu68K8f6uQuh2hEMYwQjaCj50wov9gGf40atyRGyl0OeRE/tQqZybZuP6n1jchbMIwQjSCpP/+WxEiM0vnJXA15G6m17dPjRrR0dstcDdHIYRghGiHdFis++q5noTPu0EsuMHOsAQnho9DRZcUn33MnX/IeDCNEI+TrMxdxocWMsFFaLLhmjNzlkBcSBMG+z9EH7KohL8IwQjRCpNUxb50RDY2af1rkGtLaNV+evoALLZ0yV0M0MviOSTQC2s0WfFxsazaXVsskcoWE8FFIHmuAxSriI+7kS16CYYRoBHxWUoNWswVjQ/0xZ3yo3OWQl1si7eTLrhryEgwjRCNA6r+/nTv0khtkJkdDJQBFlY04e7FV7nKIho1hhGiYGtvM+OepWgDA7VzojNwgIkiP+ZPCAXAgK3kHhhGiYdp3rBpdFhHTooMxOTJI7nLIR9xu76o5D1HkTr6kbAwjRMP0QWHP2iIcuEputHB6JHR+KpTWtaL4fJPc5RANC8MI0TCcb2xHfnk9BAFYwjBCbhSk1yBjmm3LgQ+KuJMvKRvDCNEwfNjTX58aH4Zog7/M1ZCvkaaRf3i0ChYru2pIuRhGiIZB+kQqLURF5E43TYmAwV+D2uZOfFN6Ue5yiJzGMELkpBPGJpwwNkOrVmFxUrTc5ZAP0vqpsHhGFIBLmzQSKZFTYWTLli2Ij4+HXq9HWloa8vPzBzx3+/btWLBgAUJDQxEaGoqMjIyrnk+kFNKUypumjIEhQCNzNeSrpFk1OcVGdHRZZK6GyDkOh5Hdu3cjKysL2dnZKCgoQHJyMhYuXIja2tp+zz948CDuuusufP7558jLy0NcXBx+/OMf4/x5pnhSLqtVtI8X4doiJKfU+DDEGPRo7uzG5yf6fx8m8nQOh5GXXnoJK1euxIoVK5CYmIht27YhICAAO3bs6Pf8t956Cw8++CBSUlIwdepUvPbaa7BarcjNzR128URyOXy2Aecb2xGo88O/TYuQuxzyYSqVgMyegax7OKuGFMqhMGI2m3HkyBFkZGRcegKVChkZGcjLyxvSc7S1taGrqwthYWEDntPZ2YmmpqZeX0SeRBq4uigpCnqNWuZqyNfdnmxrnfv8RB1M7V0yV0PkOIfCyIULF2CxWBAZGdnreGRkJIxG45Ce45FHHkFMTEyvQHOljRs3wmAw2L/i4uIcKZPIpczdVuw7Vg2AO/SSZ5gWHYTJkYEwW6zIKa6Wuxwih7l1Ns2mTZuwa9cuvP/++9Dr9QOet27dOphMJvtXZWWlG6skurovTtWhsa0LY4J0uG5iuNzlEEEQhEvLwxdyrxpSHofCSHh4ONRqNWpqanodr6mpQVRU1FUf+8ILL2DTpk345JNPMHPmzKueq9PpEBwc3OuLyFNI/fKZM2OgVnGHXvIMS5JtrXTflF2E0dQhczVEjnEojGi1WsyZM6fX4FNpMGp6evqAj3v++efxzDPPICcnB3PnznW+WiKZtXR247MSWxi/Yxa7aMhzxIUFYO74UIgisPcoW0dIWRzupsnKysL27dvxxhtvoKSkBKtWrUJraytWrFgBAFi+fDnWrVtnP/+5557D+vXrsWPHDsTHx8NoNMJoNKKlpWXkfgsiN/nkeyM6uqxICB+FGbEGucsh6uX2WZd28iVSEofDyNKlS/HCCy/gySefREpKCoqKipCTk2Mf1FpRUYHq6ksDqLZu3Qqz2Yyf/vSniI6Otn+98MILI/dbELnJHvvaIjEQBHbRkGe5dUY0/FQCvq9qwunaZrnLIRoyQRRFj99dqampCQaDASaTieNHSDZ1zZ1Ie/YzWEXg89/chITwUXKXRNTHf+88hAMnarHm5kn4zcIpcpdDPm6o92/uTUM0RPu+q4JVBJLHGhhEyGNJ080/OHoeCvisSQSAYYRoyPZw+XdSgFsSIxGgVaOyvh0FFY1yl0M0JAwjRENQfqEVRZWNUAnAbcncoZc8V4DWDwun25Za+IADWUkhGEaIhkDaoXf+pHBEBA28YB+RJ1jS01Xz0XfV6LJYZa6GaHAMI0SDEEURHxy1fcJkFw0pwYJJ4Rg9Sov6VjO+PH1B7nKIBsUwQjSI4vNNKK1rhc5PhYXTIwd/AJHM/NQq3DbT1p34QSG7asjzMYwQDUJaQCojMRJBeo3M1RANjbQA2ifHa9Bm7pa5GqKrYxghugqLVbQvrX17Mpd/J+WYFReCcWEBaDNb8OnxmsEfQCQjhhGiq/im9CJqmzth8NfgpikRcpdDNGS2nXx71hwp4l415NkYRoiuYk9Pf/viGdHQ+vHPhZRFGnD9xak61LeaZa6GaGB8dyXqh8Uq4p8n67D3O9snyiXsoiEFmhQRiKTYYHRbRWw+8AM+KDqPvDMXYbFyZVbyLH5yF0DkaXKKq7Fh73FUmzrsx9buLsRTS6ZjURIXPCNlmRIZhOLzTfjLV+X2Y9EGPbIzE/l6Jo/BlhGiy+QUV2PVmwW9gggA1DR1YtWbBcgprh7gkUSeJ6e4Gn8v6Du112jq4OuZPArDCFEPi1XEhr3H0V8DtnRsw97jbOImRZBez/3h65k8DcMIUY/8svo+LSKXEwFUmzqQX1bvvqKInMTXMykJwwhRj9rmgd+4nTmPSE58PZOSMIwQ9RjqBnjcKI+UgK9nUhKGEaIeqQlhCNCqB/y+ANsshNSEMPcVReSk1IQwRBv0EK5yDl/P5CkYRoh6fPK9EW1mS7/fk97QszMToVZd7e2dyDOoVQKyMxMBYMBAsv7WaXw9k0dgGCECUFnfhof//h0AYOH0SEQbejddRxn02HrPbK7LQIqyKCkaW++ZjagrXs9S/DhV2+L+ooj6wUXPyOd1Wax4aFchmju6kRIXglfung2VICC/rB61zR2ICLI1ZfMTJCnRoqRo3JIY1ev1XNXYjv/9zlH8KfcHXDthNK6dMFruMsnHMYyQz/ufT0+hoKIRQXo/bL5rFjRqW4Nh+kS+QZN3UKuEPq/nr89cxN8LzuHXu4qw/6EFCBullak6InbTkI/78ocL2PrPMwCATT+ZibiwAJkrInKPp2+fjgnho2Bs6sDD7x6FKHLxM5IPwwj5rLrmTqz9WxFEEbg7bRxuncnxIOQ7Run8sPnuWdCqVfispBY7vy6XuyTyYQwj5JOsVhH/+52jqGvuxJTIIDx5W6LcJRG53fQYAx6/dRoAYOP+Eyg+b5K5IvJVDCPkk7b/qxRfnKqDXqPC5rtnQa8ZeH0RIm+2PH08bkmMhNlixa/+WoiWzm65SyIfxDBCPqewogF/+PgkAOCpzOmYHBkkc0VE8hEEAX/46UzEGPQou9CKJ/cUy10S+SCGEfIppvYu/Oqvhei2irhtZjSWzouTuyQi2YUEaPHHu2ZBJQDvFZ7H34+ck7sk8jEMI+QzRFHEY+8dw7mGdsSF+ePZn8yAIHDtECIAmBcfhrUZkwEA6z8oxpk6LohG7sMwQj5j16FK7DtWDT+VgM13zUawXiN3SUQe5cGbJyF9wmi0mS341duF6Ojqf3sEopHGMEI+4VRNM5768HsAwG8XTkFKXIi8BRF5ILVKwMs/S0HYKC2OVzdh0z9OyF0S+QiGEfJ67WYL1rxdgM5uK26YPAYrF0yQuyQijxUZrMeL/5kMANj5dTk++d4oc0XkCxhGyOs9/dFxnKppwZggHV66Mxkq7jFDdFU3T43AygUJAIDfvvsdqhrbZa6IvB3DCHm1fd9V46/5FRAE4H/uTEF4oE7ukogU4bcLp2LmWANM7V349a4idFuscpdEXoxhhLxWZX0bHn3vOwDAgzdNxPXXhMtcEZFyaP1U2HzXLATq/JBfXo8/HTgtd0nkxRhGyCt19awm2dzRjTnjQ/HrnimLRDR040ePwrM/mQEA2HzgB3x95oLMFZG3Yhghr/TiJ6dQVNmIYL0f/vizFGjUfKkTOWNJcgyWzo2DKAJrdxfhYkun3CWRF+I7NHmdL07VYds/zwAAnv/pTIwNDZC5IiJly16SiEkRgahp6sRv3jkKURTlLom8DMMIeZXa5g5k/a0IALDs2vFYlBQtb0FEXiBA64dX7p4FrZ8Kn5+sw+tflsldEnkZhhHyGlariKzdR3GhxYypUUH2rdGJaPimRgVj/W2JAIDnck7gu3ON8hZEXoVhhLzGti/O4MvTF+CvUeOVu2dBr1HLXRKRV7knbRwWTY9Cl0XsGSDeJXdJ5CX85C6AyFkWq4j8snrUNnegsa0LL35yCgCwYcl0TIoIkrk6Iu8jCAKe+4+ZOHbehLMX2/DYe8dwV+o41LV0IiJIj9SEMKi5qCA5QRAVMBKpqakJBoMBJpMJwcHBcpdDHiCnuBob9h5Htamj1/F58aH42y/SuRsvkQsdOVuP/9yWB+sVd49ogx7ZmYkcq0V2Q71/s5uGFCenuBqr3izoE0QA4FB5Az7mXhpELlXX3NkniACA0dSBVW8WIKe42v1FkaIxjJCiWKwiNuw9joGa8wQAG/Yeh6W/d0oiGjbpb7A/0l8d/wbJUQwjpCj5ZfX9tohIRADVpg7kl9W7rygiH8K/QXIFhhFSlKEuR13bPPCbJRE5b6h/WxX1rS6uhLwJZ9OQxxNFEV+evoDNuaeRXz60T1sRQXoXV0Xkm4b6t/XMRyWoberEvfPjEazXuLgqUjqGEfJYoiji4Mk6/DH3BxRVNgIAtGoV/NQC2syWfh8jAIgy2KYYEtHIS00IQ7RBD6OpY8CxW2qVgJbObrz46Sn8+V+lWHFdPP77+gSEBGjdWispB7tpyONYrSI+/t6IJa98hRU7D6GoshE6PxVWzI/HFw/fjJfuTIYAW/C4nPTf2ZmJXOuAyEXUKgHZmbaVWPv7GxQAbP5ZCv74sxRcExGI5o5u/OnAaczfdADP5ZzgRnvUL64zQh7DYhXxj+JqvHLgNE4YmwEA/ho1lqWPx/0LEno1D/e3zgjXOCByn6H8DVqtInK+N2LzgdMoqW4CYPub/nnaODxwwwREBLM71dsN9f7NMEKy67ZY8dF31Xjl89M4XdsCAAjU+eHe68bjvusnIGxU/027l6/AytUfidxvqH+Doijis5JabD7wA747ZwIAaP1UuGteHH5500REG/zdXTq5CcMIeYSrvVl1Wax4v/A8Xv38NMovtgEAgvV+WDE/Af89PwGGAA56I/Imoijin6fq8KfcH1BQ0QjANg7sp3PHYtWNExEXFmA/lx82vAPDCMluoGbcxxZPRVNHN7YePINzDe0AgNAADe5fMAHL0sdz5D2RlxNFEV+fuYg/5f6Ab3vWI/FTCfhfs2Kx+uZJOGFsYjesl2AYIVlJS7YP9uIKD9Ri5YIJuOfa8Ril4+QuIl/zbelFbD5wGl+etq0hJAhAf3clqU1k6z2zGUgUZKj3b59993dlE6CrnlspNQ+2ZDsAqATgscXT8PO08fDXqp0rmogUL23CaKRNGI0jZxuw+cAPOHiyrt/zRFza7uGWxKhhvff5+nu0O57XUU6FkS1btuAPf/gDjEYjkpOTsXnzZqSmpg54/jvvvIP169ejvLwc11xzDZ577jksXrzY6aKHy5UzMVz13J5as8UqwtjUgYqLbaisb0NFfRsKKhquulw0AFhFYHqMgUGEiAAAc8aH4hc3TBwwjACXlppf9eYRpCaEYVxYAMaNDkBcaMCQW1Z97T1arpod5XA3ze7du7F8+XJs27YNaWlpePnll/HOO+/g5MmTiIiI6HP+119/jRtuuAEbN27EbbfdhrfffhvPPfccCgoKkJSUNKSfOZLdNAN1H4xEE6CrnlvumudPCkdF/aWwYftqR2V9G841tKHL4lxP3x9/loLbU2KdeiwReZ8Pis7joV1FTj02PFCLuLAAW0AJC+j175HBeqhVgte+R3tazZdz2ZiRtLQ0zJs3D6+88goAwGq1Ii4uDr/61a/w6KOP9jl/6dKlaG1txUcffWQ/du211yIlJQXbtm0b0V9mMBariOufOzDgp3Zp9c4vH/mRw81UrnrukXjebosVZosV5m7bV2e37b87zBYs35GPi63mAX/+QP23l9OoBYwNlf74/SGKwFvfVgz6u/115bVInzh60POIyDfknbmIu7Z/M+h5S5JjYBFF+wekxrauq56vVasQG+qPqsZ2dHZbBzwvPFCLv/0iHf5aNbRqFbR+PV9qFQSh//dXX72vDJVLxoyYzWYcOXIE69atsx9TqVTIyMhAXl5ev4/Jy8tDVlZWr2MLFy7Enj17Bvw5nZ2d6Oy8tEpfU1OTI2UOaKi7Ta5+qwBRhqsvxnNlhqs2dQzpuVf+38MYE6iDCBGiaDtu+2fPf4viZceAC82dQ3rem144CD+VcClsdFvsAWQ4O3lLv2bYKK39U0avTx6jAxDV86lDYrGKOHCidsDlorlkOxH1Z7Cl5qX3jv9ZmtLrPcfU3oXKPq23bT2tt+0wW6wouzD4xn0XWsz40Yv/7Pd7V4YT6d+7LNYhvUff89q3CA/SQSX0rFQrCLZWCAEQINiO9/y70PPvtU1De/9f9eYRRPfcswYKTZczDvF+lV9W77YPjA6FkQsXLsBisSAyMrLX8cjISJw4caLfxxiNxn7PNxqNA/6cjRs3YsOGDY6UNiRD3W0y5/uBaxuuAydqXfK8lfVtQzpPJcD+xyQCaO7oHvQxz/3HDCydN27ItUjLRa96swAC0OtNhUu2E9FAnH3vMPhrYIg1ICnW0Oc5u3vCwq5DFdjy+ZlBa9D5qWAVxT7dz+aeFmY4uZp9XulF5x44BJ8cr3HJ87pz93OPnE2zbt26Xq0pTU1NiIuLG/bzDnW3yTtSYjE21LYi4NVC5uXfOtfQjvcKzw/63HfOjcP40QH255ZSsOqyf7d9z5aaz15sxRt5Zwd93scWT0NKXEiv1K67LMXrNKqeTeYubUc01CbRcWGjBj3nSouSorH1ntl9BkdFca0AIrqKkX7v8FOrEBcWgOsnjRlSGNm5IhXpE0fDahXtAaRXF7f0ZbGgs9uKo5UmPJfT/4fxy92bPh7jR4/qafkWe7eIw9YKbe1pipa+X1HfhneOnBv0uX8yy3bPGqwRXGrpPtfQjj1Fg9+v3Ln7uUNhJDw8HGq1GjU1vVNYTU0NoqKi+n1MVFSUQ+cDgE6ng06nc6S0IRlqE+CLdyY71beXV3px0Ofe+JMZDvftfXK8ZtDnve/6BIdrHur1cLY7ZVFSNG5JjPKIaWNEpByueO9w9P1OpRKgV6mh11x9xl9awmj837zyQZ/3yczpTt1Xvjx9YdDn/sN/OnbPslhFfFs2+P3KnV3pDu3aq9VqMWfOHOTm5tqPWa1W5ObmIj09vd/HpKen9zofAD799NMBz3elwXabBJzvPnDVcyux5it/RvrE0bg9JRbpE0cziBDRkIz0ewffo13/vMPhUBgBgKysLGzfvh1vvPEGSkpKsGrVKrS2tmLFihUAgOXLl/ca4PrQQw8hJycHL774Ik6cOIGnnnoKhw8fxpo1a0but3CA1AR45QDVKIN+2FOZXPXcSqyZiMjT8D3aPTU7w6nl4F955RX7omcpKSn405/+hLS0NADATTfdhPj4eOzcudN+/jvvvIMnnnjCvujZ888/79CiZ65YDp4r5bnvuYmIPAnfo13/vBLuTUNERESyGur92+FuGiIiIqKRxDBCREREsmIYISIiIlkxjBAREZGsGEaIiIhIVgwjREREJCuGESIiIpIVwwgRERHJimGEiIiIZOXQrr1ykRaJbWpqkrkSIiIiGirpvj3YYu+KCCPNzc0AgLi4OJkrISIiIkc1NzfDYDAM+H1F7E1jtVpRVVWFoKAgCMLIbuATFxeHyspK7nnjQrzO7sNr7R68zu7B6+werrzOoiiiubkZMTExUKkGHhmiiJYRlUqFsWPHuuz5g4OD+UJ3A15n9+G1dg9eZ/fgdXYPV13nq7WISDiAlYiIiGTFMEJERESy8ukwotPpkJ2dDZ1OJ3cpXo3X2X14rd2D19k9eJ3dwxOusyIGsBIREZH38umWESIiIpIfwwgRERHJimGEiIiIZMUwQkRERLLy+jCyZcsWxMfHQ6/XIy0tDfn5+Vc9/5133sHUqVOh1+sxY8YM7N+/302VKpsj13n79u1YsGABQkNDERoaioyMjEH/v9Aljr6mJbt27YIgCLjjjjtcW6CXcPQ6NzY2YvXq1YiOjoZOp8PkyZP5/jEEjl7nl19+GVOmTIG/vz/i4uKwdu1adHR0uKlaZfriiy+QmZmJmJgYCIKAPXv2DPqYgwcPYvbs2dDpdJg0aRJ27tzp2iJFL7Zr1y5Rq9WKO3bsEL///ntx5cqVYkhIiFhTU9Pv+V999ZWoVqvF559/Xjx+/Lj4xBNPiBqNRjx27JibK1cWR6/z3XffLW7ZskUsLCwUS0pKxP/6r/8SDQaDeO7cOTdXrjyOXmtJWVmZGBsbKy5YsEC8/fbb3VOsgjl6nTs7O8W5c+eKixcvFr/88kuxrKxMPHjwoFhUVOTmypXF0ev81ltviTqdTnzrrbfEsrIy8eOPPxajo6PFtWvXurlyZdm/f7/4+OOPi++9954IQHz//feven5paakYEBAgZmVlicePHxc3b94sqtVqMScnx2U1enUYSU1NFVevXm3/b4vFIsbExIgbN27s9/w777xTvPXWW3sdS0tLE3/xi1+4tE6lc/Q6X6m7u1sMCgoS33jjDVeV6DWcudbd3d3iddddJ7722mvivffeyzAyBI5e561bt4oTJkwQzWazu0r0Co5e59WrV4s/+tGPeh3LysoS58+f79I6vclQwsjDDz8sTp8+vdexpUuXigsXLnRZXV7bTWM2m3HkyBFkZGTYj6lUKmRkZCAvL6/fx+Tl5fU6HwAWLlw44Pnk3HW+UltbG7q6uhAWFuaqMr2Cs9f66aefRkREBO677z53lKl4zlznDz/8EOnp6Vi9ejUiIyORlJSEZ599FhaLxV1lK44z1/m6667DkSNH7F05paWl2L9/PxYvXuyWmn2FHPdCRWyU54wLFy7AYrEgMjKy1/HIyEicOHGi38cYjcZ+zzcajS6rU+mcuc5XeuSRRxATE9PnxU+9OXOtv/zyS7z++usoKipyQ4XewZnrXFpaigMHDuDnP/859u/fj9OnT+PBBx9EV1cXsrOz3VG24jhzne+++25cuHAB119/PURRRHd3N375y1/isccec0fJPmOge2FTUxPa29vh7+8/4j/Ta1tGSBk2bdqEXbt24f3334der5e7HK/S3NyMZcuWYfv27QgPD5e7HK9mtVoRERGBP//5z5gzZw6WLl2Kxx9/HNu2bZO7NK9y8OBBPPvss3j11VdRUFCA9957D/v27cMzzzwjd2k0TF7bMhIeHg61Wo2amppex2tqahAVFdXvY6Kiohw6n5y7zpIXXngBmzZtwmeffYaZM2e6skyv4Oi1PnPmDMrLy5GZmWk/ZrVaAQB+fn44efIkJk6c6NqiFciZ13R0dDQ0Gg3UarX92LRp02A0GmE2m6HVal1asxI5c53Xr1+PZcuW4f777wcAzJgxA62trXjggQfw+OOPQ6Xi5+uRMNC9MDg42CWtIoAXt4xotVrMmTMHubm59mNWqxW5ublIT0/v9zHp6em9zgeATz/9dMDzybnrDADPP/88nnnmGeTk5GDu3LnuKFXxHL3WU6dOxbFjx1BUVGT/WrJkCW6++WYUFRUhLi7OneUrhjOv6fnz5+P06dP2sAcAp06dQnR0NIPIAJy5zm1tbX0ChxQARW6zNmJkuRe6bGisB9i1a5eo0+nEnTt3isePHxcfeOABMSQkRDQajaIoiuKyZcvERx991H7+V199Jfr5+YkvvPCCWFJSImZnZ3Nq7xA4ep03bdokarVa8d133xWrq6vtX83NzXL9Corh6LW+EmfTDI2j17miokIMCgoS16xZI548eVL86KOPxIiICPF3v/udXL+CIjh6nbOzs8WgoCDxr3/9q1haWip+8skn4sSJE8U777xTrl9BEZqbm8XCwkKxsLBQBCC+9NJLYmFhoXj27FlRFEXx0UcfFZctW2Y/X5ra+9vf/lYsKSkRt2zZwqm9w7V582Zx3LhxolarFVNTU8VvvvnG/r0bb7xRvPfee3ud/7e//U2cPHmyqNVqxenTp4v79u1zc8XK5Mh1Hj9+vAigz1d2drb7C1cgR1/Tl2MYGTpHr/PXX38tpqWliTqdTpwwYYL4+9//Xuzu7nZz1crjyHXu6uoSn3rqKXHixImiXq8X4+LixAcffFBsaGhwf+EK8vnnn/f7nitd23vvvVe88cYb+zwmJSVF1Gq14oQJE8S//OUvLq1REEW2bREREZF8vHbMCBERESkDwwgRERHJimGEiIiIZMUwQkRERLJiGCEiIiJZMYwQERGRrBhGiIiISFYMI0RERCQrhhEiIiKSFcMIERERyYphhIiIiGTFMEJERESy+v+qAsYFTTybRwAAAABJRU5ErkJggg==",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import math\n",
        "\n",
        "def initial_cond(x, L):\n",
        "    return np.exp(-(x-L/2)**2/0.02)\n",
        "\n",
        "L, N = 1, 20\n",
        "d = L / N\n",
        "x = np.linspace(0, L, N+1)\n",
        "y = initial_cond(x, L)\n",
        "plt.scatter(x,y)\n",
        "plt.plot(x,y)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "0ksIjOCPhxyc",
        "outputId": "793af0a3-ef48-4d7c-d1fb-d660c5afa29c"
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x10be4898>]"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": "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",
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "def initial_cond(x, L):\n",
        "    return math.exp(-(x-L/2)**2/0.02)\n",
        "\n",
        "L, N = 1, 20\n",
        "d = L / N\n",
        "\n",
        "u = np.arange(N+1, dtype=float)\n",
        "v = np.arange(N+1, dtype=float)\n",
        "C = 0.5\n",
        "x = np.linspace(0, L, N + 1)\n",
        "\n",
        "for i in range(0, N + 1):\n",
        "  u[i] = initial_cond(x[i], L) *.01\n",
        "\n",
        "v[0], v[N] = 0, 0\n",
        "for i in range(0, N -1 ):\n",
        "  v[i+1] = u[i+1] + C * (u[i+2] - 2 * u[i+1] + u[i])\n",
        "\n",
        "\n",
        "plt.scatter(x, v)\n",
        "plt.plot(x, v)\n",
        "plt.plot(x, u)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {},
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "colab": {
      "provenance": []
    },
    "kernelspec": {
      "display_name": "Python 3",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.8.5"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}
